Chile won the Copa America title on penalties on Saturday night, leaving Messi still waiting for his first major title with Argentina as they fell at the final hurdle, just as they did in the World Cup last year.
But PSG forward Lavezzi said he is confident the 28-year-old is destined to taste success with his country.
“At some point Leo [Messi] is going to win something with Argentina,” he told reporters.
“We thought this was an opportunity to make our mark, but unfortunately we could not. It hurts a lot.”
Gonzalo Higuain and Ever Banega missed in the shoot-out before Alexis Sanchez’s ‘Panenka’ finish sealed the hosts’ first-ever Copa America triumph.
Lavezzi admitted they thought they would finally fulfil their potential in Santiago, and said they are heading in the right direction.
“Once again we are left with a bitter taste,” he added. “It hurts because we believed that this was the chance to win something.
“I think that we should continue on this path. We are all very good in terms of the group. We are just missing that little step to achieve something.”